Oscillations of a disc with a smaller disc removed (Feynman ex. 17.23)

  • #1
ergospherical
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Homework Statement
Determine the period of small oscillations, given that the disc rolls without slipping
Relevant Equations
N/A
A disc of radius has a smaller disc of radius removed. The resulting object has mass :

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The centre of mass is a distance from the edge. The moment of inertia of the shape about the centre istherefore the moment of inertia about is If the angle through which the disc has rotated is denoted , then the centre of mass has velocityTherefore the kinetic energy of the body isMeanwhile, the height of the centre of mass when the body has rotated by istherefore the potential energy is . Overall I write the energy asThe motion does not look simple harmonic, at least for finite . To investigate we can put and , and I assume also , which givesHowever in the solution manual they write ?
 
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  • #2
State the parallel axis theorem. Did you use it correctly?
 
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  • #3
haruspex said:
State the parallel axis theorem. Did you use it correctly?
ahhhh, kill me
ought to be , right?

[Edit: Yep, I checked it through with and it works. Thanks haru! ☺️]
 
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